Toroidal families and averages of L-functions, I

Étienne Fouvry; Emmanuel Kowalski; Philippe Michel

Toroidal families and averages of L-functions, I

Number Theory 2024-05-27 v3

Authors: Étienne Fouvry , Emmanuel Kowalski , Philippe Michel

Abstract

We initiate the study of certain families of $L$ -functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values $L(\demi,\chi^a)L(\demi,\chi^b)$ for arbitrary integers~ $a$ and~ $b$ when $\chi$ varies over Dirichlet characters to a prime modulus.

Keywords

l-functions torus characters dirichlet characters central point family averages prime modulus

Cite

@article{arxiv.2303.11664,
  title  = {Toroidal families and averages of L-functions, I},
  author = {Étienne Fouvry and Emmanuel Kowalski and Philippe Michel},
  journal= {arXiv preprint arXiv:2303.11664},
  year   = {2024}
}

Comments

29 pages; v3 (final version, to appear in Acta Arithmetica in volume dedicated to Henryk Iwaniec)

Toroidal families and averages of L-functions, I

Abstract

Keywords

Cite

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